If nothing else, the timing of “Chappaquiddick,” a film about a tragedy and the infamous scandal that spun out of it almost 50 years ago, seems odd.

Why this story, about a drunk driving accident that killed a pretty young woman in the car alone with a married, rising star U.S. Senator with that magical Kennedy surname, and why now?

But ducking into a matinee of it you see the cunning of Entertainment Studios chief Byron Allen, the former comic who has aimed his operation at niche pictures ranging in quality from “Hurricane Heist” and “Friend Request” to “47 Meters Down” and “Hostiles.” The audience I saw it with was entirely white and quite old.

Allen’s financed a film aimed at conservatives in need of a safe space at the cinemas where they can escape the tidal wave of TV news and its indictments, investigations and reminders of their very poor judgement.

And if nothing else it’s to be praised for putting a face and person behind a name that history has bandied about like a political football for all these decades — Mary Jo Kopechne. Kate Mara, of the equally dynastic NFL franchise-owner Maras, shows Kopechne as an idealist, a professional, still broken up by the death of Bobby Kennedy the summer before, compassionate to the surviving Kennedy brother, Ted (Jason Clarke) who seems to shun the mantle his tyrannical dad (Bruce Dern) has put on him.

“Lead a serious life.”

The old man has had a stroke, but with three presidency-bound brothers dead before, Ted, the hard drinking, womanizing and callow youngest brother has a family brand to protect. He just doesn’t seem to want that, or welcome the “Kennedy ’72” talk one and all bandy about on this weekend of a small boat sailing regatta and Martha’s Vineyard reunion of the extended Kennedy family.

“Family,” as Ted describes it to the partiers at a cottage on Chappaquiddick Island (at the seaward end of Martha’s Vineyard), includes cousins like his lawyer “Joey will fix it” Gargan (Ed Helms), a like-minded state’s attorney (Jim Gaffigan) and “The Boiler Room Girls,” younger female campaign aides who flock to the Kennedy name like Elaine on that infamous “Seinfeld” episode.

Mara and Olivia Thirlby play two of those women, practical idealists whose professionalism trumps any hint of sexual opportunism that this reunion has had attached to it by conspiracy buffs, the film suggests.

“How’re your kids, Senator? How’s your WIFE?”

The accident happens after a lot of drinks and a heart to heart talk about expectations, burdens, grief and ideals. Nothing more. No wonder Fox News hasn’t been all over this one. Well, that and the fact that Producer Allen is a black man.

And as Kennedy has foretold, talking of “character” and the ways it is tested, it’s what happens after that Oldsmobile flips into Poncha Pond in the middle of the night that reveals his.

Kennedy, 37, was still lightly regarded by many insiders, still called “Teddy” by the likes of Ted Sorensen (Taylor Allen), veteran insider and family public relations strategist. Teddy’s closest pals, the lawyers played by funnymen Helms and Gaffigan, try to get the vacuum-sealed car doors open after the Senator staggers back to the party cottage. They direct him to do the right thing, row him across the bay to the mainland to report the crash to the police.

And that’s not what Kennedy, not-entirely-sober, certainly in shock and overwhelmed by the growing understanding of what this means to his career, does. He calls his old man, who can’t speak more than a word or two. His one word edict?

“Alibi!”

“Chappaquiddick” then becomes a master class on political spin, damage control and image management. Formidable character actor Clancy Brown (“The Shawshank Redemption”) is the the take-charge guy of the Ten Angry Spin Doctors summoned by Old Joe to “handle” this.

No, Brown doesn’t look anything like former Defense Secretary Robert McNamara. But that’s a mere quibble compared to what we see presented as unvarnished fact in a movie that strays from that straight and narrow too often for its own good.

“Chappaquiddick” is more factual than “JFK,” less on-the-nose than “W,” on the sliding Oliver Stone scale of historical accuracy. There’s a lot we don’t actually know about the accident, and while the movie sometimes sensationalizes the grey areas, the fact that the Kennedy clan and the future “Lion of the Senate” saw to it that we will never know is undisputable.

As is the naked power play and value of family connections that we see as various “fixers” “get ahead of the story” in their efforts to “control the body,” bums’ rush the police investigation and prosecution and generally clear the ground for a Kennedy “comeback” before the poor woman even has her funeral.

This stuff is documented, and if anything alarms a country that has gullibly embraced political dynasties since its founding, it should be these scenes.

What works against “Chappaquiddick” is its lack of narrative drive, that drum I beat far too often — urgency. Curran is a slack filmmaker saddled with an ugly story, cynically told, and a generally unlikeable “hero.” Clarke, of “Winchester” and “Dawn of the Planet of the Apes,” is a reliable character actor without a lot of screen charisma. Here, he doesn’t even bother to master the Kennedy patrician Back Bay accent. He’s built up into a villain who hardly seems worthy of that label.

Clarke’s a leading man like Teddy was presidential timber. Not really.

The speculation about Kopechne’s manner of death tends towards the graphic and lurid, even if it’s fair game.

That makes for a movie that has quality and some value. It’s just not one you warm to. Even Helms, playing “the conscience” Teddy chooses to ignore, seems more a conservative construct than a real person.

We don’t know what we don’t know, Donald Rumsfeld famously said. But in this case, we know enough. Wandering into the unknowns doesn’t serve history or the film well enough to make “Chappaquiddick” anything more than cinematic escape for folks who don’t like the current history they’d rather avoid thinking about by going to the movies.